Optimal job scheduling is a class of optimization problems related to scheduling. The inputs to such problems are a list of jobs (also called processes or tasks) and a list of machines (also called processors or workers). The required output is a schedule – an assignment of jobs to machines. The schedule should optimize a certain objective function. In the literature, problems of optimal job scheduling are often called machine scheduling, processor scheduling, multiprocessor scheduling, or just scheduling.
There are many different problems of optimal job scheduling, different in the nature of jobs, the nature of machines, the restrictions on the schedule, and the objective function. A convenient notation for optimal scheduling problems was introduced by Ronald Graham, Eugene Lawler, Jan Karel Lenstra and Alexander Rinnooy Kan.[1][2] It consists of three fields: α, β and γ. Each field may be a comma separated list of words. The α field describes the machine environment, β the job characteristics and constraints, and γ the objective function.[3] Since its introduction in the late 1970s the notation has been constantly extended, sometimes inconsistently. As a result, today there are some problems that appear with distinct notations in several papers.
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